After unlock at&t's iphone, could I use Verizon's SIM card?

I just did not understand about that unlock, one unlocked phone can use any kind of company's SIM card? I mean can a at&t's phone, after unlock it, can I use verizon, t-mobile, sprint's SIM card?

Yes, only if the unlock is factory clean IMEI unlock. Which will allow you to use any Gsm network round the world

Verizon and Sprint are CDMA networks. They don't use sim cards, and you can't use a GSM phone with them.